Statistical analysis reveals co-expression patterns of many pairs of genes in yeast are jointly regulated by interacting loci.

Expression quantitative trait loci (eQTL) studies have generated large amounts of data in different organisms. The analyses of these data have led to many novel findings and biological insights on expression regulations. However, the role of epistasis in the joint regulation of multiple genes has not been explored. This is largely due to the computational complexity involved when multiple traits are simultaneously considered against multiple markers if an exhaustive search strategy is adopted. In this article, we propose a computationally feasible approach to identify pairs of chromosomal regions that interact to regulate co-expression patterns of pairs of genes. Our approach is built on a bivariate model whose covariance matrix depends on the joint genotypes at the candidate loci. We also propose a filtering process to reduce the computational burden. When we applied our method to a yeast eQTL dataset profiled under both the glucose and ethanol conditions, we identified a total of 225 and 224 modules, with each module consisting of two genes and two eQTLs where the two eQTLs epistatically regulate the co-expression patterns of the two genes. We found that many of these modules have biological interpretations. Under the glucose condition, ribosome biogenesis was co-regulated with the signaling and carbohydrate catabolic processes, whereas silencing and aging related genes were co-regulated under the ethanol condition with the eQTLs containing genes involved in oxidative stress response process.